IMAGE  EVALUATION 
TEST  TARGET  (MT-3) 


1.0 


I.I 


^1^  iM 

■-    In    1111122 

^  ti&  lllllio 


1.8 


1.25 


U    ill  1.6 


-    6 " 


Photographic 

Sciences 
Corporation 


23  WEST  MAIN  STREET 

WEBSTER,  NY.  14580 

(716)  872-4503 


f,' 


&y 


«' 


CIHM/ICMH 

Microfiche 

Series. 


CIHM/ICMH 
Collection  de 
microfiches. 


Canadian  Institute  for  Historical  Microreproductions  /  Institut  Canadian  de  microreproductions  historiques 


»i':*-!!. 


Technical  and  Bibliographic  Notes/Notes  techniques  et  bibliographiques 


The  Institute  has  attempted  to  obtain  the  best 
original  copy  available  for  filming.  Features  of  this 
copy  which  may  be  bibliographically  unique, 
which  may  alter  any  of  the  images  in  the 
reproduction,  or  which  may  significantly  change 
the  usual  method  of  filming,  are  checked  below. 


L'Institut  a  microfilm^  le  meilleur  exemplaire 
qu'il  lui  a  dtd  possible  de  se  procurer.  Les  details 
de  cet  exemplaire  qui  sont  peut-§tre  uniques  du 
point  de  vue  bibliographique,  qui  peuvent  modifier 
une  image  reproduite,  ou  qui  peuvent  exiger  une 
modification  dans  la  mdthode  normale  de  filmage 
sont  indiquds  ci-dessous. 


D 


Coloured  covers/ 
Couverture  de  couleur 


I      I    Covers  damaged/ 


Couverture  endommag^e 


I      I    Covers  restored  and/or  laminated/ 


Couverture  restaur^e  et/ou  pellicul6e 


Cover  title  missing/ 

Le  titre  de  couverture  manque 


H 


I      I    Coloured  maps/ 


□    Coloured  pages/ 
Pages  de  couleur 


Cartes  g^ographiques  en  couleur 


D 
D 

D 
D 


Pages  damaged/ 
Pages  endommagdes 

Pages  restored  and/or  laminated/ 
Pages  restaurdes  et/ou  pelliculdes 

Pages  discoloured,  stained  or  foxed/ 
Pages  d6color6es,  tachet^es  ou  piqudes 

Pages  detached/ 
Pages  d^tachdes 


D 


Coloured  ink  (i.e.  other  than  blue  or  black)/ 
Encre  de  couleur  (i.e.  autre  que  bleue  ou  noire) 


□    Showthrough/ 
Transparence 


□    Coloured  plates  and/or  illustrations/ 
Planches  et/ou  illustrations  en  couleur 


D 


Bound  with  other  material/ 
Relid  avec  d'autres  documents 


D 
D 


Quality  of  print  varies/ 
Quality  indgale  de  I'impression 

Includes  supplementary  material/ 
Comprend  du  matdriel  supplementaire 


D 


D 


Tight  binding  may  cause  shadows  or  distortion 
along  interior  margin/ 

La  re  liure  serrde  peut  causer  de  I'ombre  ou  de  la 
distortion  le  long  de  la  marge  intdrieure 

Blank  leaves  added  during  restoration  may 
appear  within  the  text.  Whenever  possible,  these 
have  been  omitted  from  filming/ 
II  se  peut  quG  certainos  pages  blanches  ajoutdes 
lors  d'une  restauration  apparaissent  dans  le  texte, 
mais,  lorsque  cela  6tait  possible,  ces  pages  n'ont 
pas  dtd  filmdes. 


D 
D 


Only  edition  available/ 
Seule  Edition  disponible 

Pages  wholly  or  partially  obscured  by  errata 
slips,  tissues,  etc.,  have  been  refilmed  to 
ensure  the  best  possible  image/ 
Les  pages  totalement  ou  partiellement 
obscurcies  par  un  feuillet  d'errata,  une  pelure, 
etc.,  ont  6t6  filmdes  d  nouveau  de  fapon  d 
obtenir  la  meilleure  image  possible. 


D 


Additional  comments:/ 
Commentaires  suppl6menraires; 


This  item  is  filmed  at  the  reduction  ratio  checked  below/ 

Ce  document  est  film^  au  taux  de  reduction  indiqud  ci-dessous. 

10X  14X  18X  22X 


26X 


SOX 


12X 


16X 


20X 


28X 


32X 


ails 

du 

tdifier 

une 

nage 


rata 
o 


>elure. 
Id 


H 


32X 


The  copy  filmed  here  has  been  reproduced  thanks 
to  the  generosity  of: 

Library  of  Congress 
Photoduplication  Service 

The  images  appearing  here  are  the  besi  quality 
possible  considering  the  condition  and  legibility 
of  the  original  copy  and  in  keeping  with  the 
filming  contract  specifications. 


Original  copies  in  printed  paper  covers  are  filmed 
beginning  with  the  front  cover  and  ending  on 
the  last  page  with  a  printed  or  illustrated  impres- 
sion, or  the  back  cover  when  appropriate.  All 
other  original  copies  are  filmed  beginning  on  the 
first  page  with  a  printed  or  illustrated  impres- 
sion, and  ending  on  the  last  page  with  a  printed 
or  illustrated  impression. 


The  last  recorded  frame  on  each  microfiche 
shall  contain  the  symbol  —^^  (meaning  "CON- 
TINUED"), or  the  symbol  V  (meaning  "END"), 
whichever  applies. 

Maps,  plates,  charts,  etc.,  may  be  filmed  at 
different  reduction  ratios.  Those  too  large  to  be 
entirely  included  in  one  exposure  are  filmed 
beginning  in  the  upper  left  hand  corner,  left  to 
right  and  top  to  bottom,  as  many  frames  as 
required.  The  following  diagrams  illustrate  the 
method: 


1  2  3 


L'exemplaire  film6  fut  reproduit  grdce  d  la 
g6n6rosit6  de: 

Library  of  Congress 
Photoduplication  Service 

Les  images  suivantes  ont  6t6  reproduites  avec  le 
plus  grand  soin,  compte  tenu  de  la  condition  et 
de  la  nettetd  de  l'exemplaire  filmd,  et  en 
conformity  avec  les  conditions  du  contrat  de 
filmage. 

Les  exemplaires  originaux  dont  la  couverture  en 
papier  est  imprim6a  sont  filmds  en  commen9ant 
par  le  premier  plat  et  en  terminant  soit  par  la 
derniilire  page  qui  comporte  une  empreinte 
d'impression  ou  d'illustration,  soit  par  le  second 
plat,  salon  le  cas.  Tous  les  autres  exemplaires 
originaux  sont  filmds  en  commenpant  par  la 
premidre  page  qui  comporte  une  empreinte 
d'impression  ou  d'illustration  et  en  terminant  par 
la  dernidre  page  qui  comporte  une  teiie 
empreinte. 

Un  des  symboles  suivants  apparaitra  sur  la 
dernidre  image  de  cheque  microfiche,  selon  le 
cas:  le  symhr :?  —m-  signifie  "A  SUIVRE",  le 
symbole  V  fcjgnifie  "FIN". 

Les  cartes,  planches,  tableaux,  etc.,  peuvent  dtre 
film6s  d  des  taux  de  reduction  diffdrents. 
Lorsque  le  document  est  trop  grand  pour  dtre 
reproduit  en  un  seul  clich6,  il  est  filmd  d  partir 
de  Tangle  supdrieur  gauche,  de  gauche  d  droite, 
et  de  haut  en  bas,  en  prenant  le  nombre 
d'Images  ndcessaire.  Les  diagrammes  suivants 
iilustrent  la  mdthode. 


1 

2 

3 

4 

5 

6 

i 


^ 


U.  S,    Ho^^^'-'^    ^- 


-^-^    ^       9^^     ^^»  1> 


coK^EECTionsrs 


TO 


HANSEN'S  TABLES  OF  THE  MOON. 


PREPARED  AND  PRINTED 


FOR  THE  UBlt  OF  THE 


■i 


AMERICAN  EPHEMERIS  AND  NAUTICAL  ALMANAC. 


i 


WASHINGTON : 

aOVERNMENT   PRINXrNO   OFFICE. 

1878. 


..-^ 


In  the  RcsearcheH  on  ihe  Motion  of  the  Moon*  to  Im'  |)ro(»tUit<Kl  in  Api^ndix  IT  of  the  Washington  Observations  for 
1875,  it  is  Hhown  that  the  larjfe  deviations  of  Hanson's  hmar  tahles  from  oKservations  will  almost  entirely  disappear 
by  substituting  for  the  empirical  term  an  eini)irical  alteration  of  the  other  term  (hie  to  the  action  of  Venus,  and  by 
making  suitable  alterations  in  the  elements  of  mean  motion.  The  entire  secular  and  long  \v:v'\od  tmrecstions  may  be 
formuljite<l  as  follows:     Put 


Vj  =  21".47  sin  (8  V  —  13  E  +  274°  14'). 

(The  on>iririe}d  term.)  (Vy 

A  ==  18  V  -  16  E  -  (/. 

T  =  time  after  1800.0,  counted  in  centuries. 

Then  the  sum  of  the  corrections  in  question  is : 

—  Vj— l'M4  — 2y".17T  — 3".76T'^-15".5cos  A.        o 

For  the  present  purposes,  the  most  convenient  way  of  applying  these  corrections  is  to  omit  Table  XLI,  Arg.  30, 
which  contains  V,,  and  to  rephu-e  it  by  the  sum  of  the  above  terms,  omitting  the  first ;  this  sum  being  tabulated  as  a 
function  of  the  time.  Table  XLI,  liowever,  contains  the  constiuit  21".49,  which  will  hi  oniittetl  with  the  table,  and 
must  therefore  l)e  ajjplied  in  the  new  table.     The  quantity  by  which  table  XLI  must  be  replaced  is  therefore 

20".36  -  29".17  T  —  3".76  T^  —  16".5  cos  A. 

this  is  to  be  reduced  to  Hansen's  units  by  lx;ing  multiplied  by  the  factor  212.6.  The  result  is  shown  for  the  Iwginning 
of  each  tenth  year  of  the  present  century,  and  interiM>lated  to  every  year  from  1880  to  1900  in  the  first  of  the  follow- 
ing tiibles. 

This  is  followed  by  a  corrected  table  XXXIV,  in  which  the  t«rm 

0".335  sin  (2  «7  —  4  .7'  +  2  w  —  4  to'), 

is  removed  and  replaced  by 

—  0".285  sin  i2g  —  4  .9'  +  2  w  —  4  w'), 

conformably  to  the  results  given  on  p.  439  of  Hansen's  Darleffung.     lieducing  the  correction  to  Hansen's  units,  it  is 

—  131  sin  (2  «7  —  4  (7'  +  2  «j  —  4  w'). 

This  quantity  being  tabulated  and  applied  to  Hansen's  Table  XXXIV,  we  have  the  corrected  table  here  given. 

No  further  corrections  than  these  are  now  proposetl,  because  they  would  of  necessity,  in  the  present  stiite  of  the 
lunar  theory,  ha  purely  provisional,  and  would  prove  a  sounti  of  trouble  in  revising  the  theory. 

With  these  corrections  it  is  intended  to  employ  Hansen's  Tables  in  the  Americsin  Ephenieris  for  1883. 

SIMON  NEWCOMB. 


'  Abstract  in  Sillinian's  Juuntal  for  November,  1877. 


)bscrvation8  for 

tirely  disappear 

Vonus,  and  by 

'iHitioiis  may  be 


XLI,  Arg.  30, 
a;  tabulated  as  a 
li  tlie  table,  and 
jrofore 


r  the  lieginning 
it  of  the  follovv- 


TABLE  XLI. 
Argument.     The  year  of  the  Chriitian  era. 


Year. 

Ineq. 

Year. 

Ineq. 

1800 

+7603 

1880 

-223s 

—  768 

—  146 

1810 

6835 

1 881 

—  2381 

—  946 

-'45 

1820 

5889 

1882 

—2526 

— mo 

-145 

1830 

4779 

1883 

—  2671 

—1256 

—144 

1840 

3523 

1884 

-2815 

—'363 

-144 

1850 

2160 

1885 

-2959 

—1446 

-143 

i860 

+  714 

1886 

— 3102 

—1473 

—"43 

1870 

—  759 

1887 

-3245 

—1476 

—142 

1880 

-2235 

1888 

-3387 

—1433 

-  141 

1890 

-3668 

1889 

-3528 

-'356 

— 140 

1900 

—5024 

1890 

—3668 

isen's  units,  it  is 


re  given. 

tent  stiite  of  the 

883. 
^COMB. 


%r 


/ 


